I make a tadhka with my lentils. It is a bit of butter melted in some oil with spices. This I add to my lentils to make dal fry, would this be kosher?
I know meat and dairy should not mix, but what vegetables and dairy?
Those ingredients are totally kosher. People cook dairy with vegetables all the time.
Check out this menu from a vegetarian Indian restaurant in Cincinnati, certified kosher by the rabbis there. Plenty of butter-and-legumes combinations.
Of course, a dish is only actually kosher if the equipment used to make it is kosher. So if you make your own dal fry and bring it to the office, don't expect your more-observant Jewish colleagues to eat it. (Though there are some who are less meticulous who would say "eh the ingredients are okay, good enough.")
(Just thinking here ... lentils are described as a dietary staple throughout the Talmud; and there was some sort of dairy condiment that was also very common in the Talmud ... but I can't think of a place where it happens to mention both together. But anyhow -- it's perfectly kosher, even if we don't have documentation that they ate that particular combination.)
No problem at all with dairy and vegetables or with meat and vegetables. Any vegetables cooked with dairy (as opposed to mixed together when cold) will generally cause the pots used to become dairy (same for meat) and therefore have limitations on using those same pots with meat (or dairy in the reverse) or for pareve - not meat or dairy - to be eaten together with meat (or dairy).
However, the question is not as strange as some others might think. There is a rule about not baking bread that is either meat or dairy. Because bread is eaten frequently with all kinds of other foods, bread itself is normally baked 100% pareve. There are certain exceptions, but generally most mainstream supervising organizations will not certify bread that is meat or (more commonly for non-kosher bread) dairy. That actually limits some bakeries - for example, my local Costco has a OK certified bakery but the bagels are not marked as kosher because the entire bakery is treated as dairy and there is no supervision or strict division of equipment to ensure that the bagels are always pareve, though my understanding is that they almost certainly are actually pareve. (I had a customer once with a much larger mostly dairy bakery and the Kof-K did certify that the bagels were kosher and pareve, as the factory had entirely separate ovens and other equipment for bagels.)
Based on Taz (97:1), the tadkha could be prohibited due to the risk of eating them together with meat – specifically if we assume that tadhka is typically eaten with meat dishes. We see this concept in the Gemara that prohibits consuming bread kneaded with milk. However, there are opinions that limit this stringency only to bread, which is the dietary staple of man.